Chapter 8
Production
Chapter Outline
• The Input-Output Relationship of The
Production Function
• Production In The Short Run
• Total, Marginal, and Average Products
• Production In The Long Run
• Returns To Scale
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The Production Function
• Production function: the relationship that
describes how inputs like capital and labor are
transformed into output.
• Mathematically,
Q = F (K, L)
K = Capital
L = Labor
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Figure 8.1: The Production Function
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Fixed and Variable Inputs
• Long run: the shortest period of time required to alter the
amounts of all inputs used in a production process.
• Short run: the longest period of time during which at least
one of the inputs used in a production process cannot be
varied.
• Variable input: an input that can be varied in the short run.
• Fixed input: an input that cannot vary in the short run.
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Production in the Short Run
• Three properties:
1.It passes through the origin
2.Initially the addition of variable inputs augments
output an increasing rate
3.beyond some point additional units of the
variable input give rise to smaller and smaller
increments in output.
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Figure 8.2: A Specific Short-Run
Production Function
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Figure 8.3: Another Short-Run
Production Function
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An Important Characteristic of
Short-Run Production Functions
• Law of diminishing returns: if other inputs
are fixed, the increase in output from an
increase in the variable input must
eventually decline.
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Figure 8.4: The Effect of Technological
Progress in Food Production
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Short-Run Production Function
Components
• Total product curve: a curve showing the amount
of output as a function of the amount of variable
input.
• Marginal product: change in total product due to a
1-unit change in the variable input.
• Average product: total output divided by the
quantity of the variable input.
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Figure 8.5: The Marginal Product
of a Variable Input
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Relationships Among Total, Marginal
and Average Product Curves
• When the marginal product curve lies above the
average product curve, the average product curve
must be rising
• When the marginal product curve lies below the
average product curve, the average product curve
must be falling.
• The two curves intersect at the maximum value of
the average product curve.
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Figure 8.6: Total, Marginal, and
Average Product Curves
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The Practical Significance of the
Average Marginal Distinction
• Suppose you own a fishing fleet consisting of a given
number of boats, and can send your boats in whatever
numbers you wish to either of two ends of an extremely
wide lake, east or west. Under your current allocation of
boats, the ones fishing at the east end return daily with 100
pounds of fish each, while those in the west return daily
with 120 pounds each. The fish populations at each end of
the lake are completely independent, and your current
yields can be sustained indefinitely.
• Should you alter your current allocation of boats?
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The Practical Significance Of The
Average Marginal Distinction
• The general rule for allocating an input
efficiently in such cases is to allocate the
next unit of the input to the production
activity where its marginal product is
highest.
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Production In The Long Run
• Isoquant: the set of all input combinations
that yield a given level of output.
• Marginal rate of technical substitution
(MRTS): the rate at which one input can be
exchanged for another without altering the
total level of output.
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Figure 8.7: Part of an Isoquant Map for
the Production Function
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Figure 8.8: The Marginal Rate
of Technical Substitution
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Figure 8.9: Isoquant Maps for Perfect
Substitutes and Perfect Complements
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Returns To Scale
• Increasing returns to scale: the property of a production
process whereby a proportional increase in every input
yields a more than proportional increase in output.
• Constant returns to scale: the property of a production
process whereby a proportional increase in every input
yields an equal proportional increase in output.
• Decreasing returns to scale: the property of a production
process whereby a proportional increase in every input
yields a less than proportional increase in output.
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Figure 8.10: Returns to Scale Shown on
the Isoquant Map
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Figure 8.A.1: Effectiveness vs. Use:
Lobs and Passing Shots
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Figure 8A2: The Optimal Proportion
of Lobs
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Figure 8A.3: At the Optimizing Point, the
Likelihood of Winning with a Lob is Much
Greater than of Winning with a Passing Shot
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Figure 8A.4: The Production Mountain
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Figure 8A.5: The Isoquant Map Derived
from the Production Mountain
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Some Examples of Production
Functions
• The Cobb-Douglas Production Function
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Some Examples of Production
Functions
• The Leontief, or Fixed-Proportions, Production
Function
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Figure 8A6: Isoquant Map for the CobbDouglas Production Function Q = K½L½
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Figure 8A.7: Isoquant Map for the Leontief
Production Function Q = min (2K,3L)
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A Mathematical Definition of Returns
to Scale
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